The aim of the dissertation is to extend on the work done by Hydon in [17]. We
only consider second order ordinary difference equations and calculate their symmetry
generators, first integrals and reduce their order, that is, find a general solution.
We investigate the association between a symmetry generator and a first integral.
Furthermore, we investigate when a reduced equation may be further reduced and
lead to a double reduction. The examples considered are obtained from [17].
ii
